Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence.
Soit la compactification merveilleuse d’un groupe semi-simple , connexe, de type adjoint, algébrique défini sur un corps de nombre . Nous démontrons l’asymptotique conjecturée par Manin du nombre de points -rationnels sur de hauteur plus petite que , lorsque , et construisons de manière explicite une mesure sur , généralisant celle de Peyre, qui décrit la répartition asymptotique des points rationnels sur . Ce travail repose sur la propriété de mélange de , qui est démontrée avec une estimée de vitesse.
@article{ASENS_2008_4_41_3_385_0, author = {Gorodnik, Alex and Maucourant, Fran\c{c}ois and Oh, Hee}, title = {Manin's and {Peyre's} conjectures on rational points and adelic mixing}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {385--437}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 41}, number = {3}, year = {2008}, doi = {10.24033/asens.2071}, mrnumber = {2482443}, zbl = {1161.14015}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2071/} }
TY - JOUR AU - Gorodnik, Alex AU - Maucourant, François AU - Oh, Hee TI - Manin's and Peyre's conjectures on rational points and adelic mixing JO - Annales scientifiques de l'École Normale Supérieure PY - 2008 SP - 385 EP - 437 VL - 41 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2071/ DO - 10.24033/asens.2071 LA - en ID - ASENS_2008_4_41_3_385_0 ER -
%0 Journal Article %A Gorodnik, Alex %A Maucourant, François %A Oh, Hee %T Manin's and Peyre's conjectures on rational points and adelic mixing %J Annales scientifiques de l'École Normale Supérieure %D 2008 %P 385-437 %V 41 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2071/ %R 10.24033/asens.2071 %G en %F ASENS_2008_4_41_3_385_0
Gorodnik, Alex; Maucourant, François; Oh, Hee. Manin's and Peyre's conjectures on rational points and adelic mixing. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 3, pp. 385-437. doi : 10.24033/asens.2071. http://www.numdam.org/articles/10.24033/asens.2071/
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